In its inflated state, the gas bag in such a head protection restraining system is tensioned between the A and C columns, since the increase in volume during the inflation process implies a simultaneous contraction in length. In its tensioned state the gas bag ensures lateral support even with burst windowpanes. As a result of unavoidable leakage losses and/or an intentional gas discharge to dissipate impact energy, the gas bag then relaxes so that it regains its original length and its lower edge hangs down loosely.